1. Field of the Invention
This invention relates to amplification circuits and, more particularly, to circuits for providing linear bandpass amplification of high frequency signals by interferometric techniques.
2. Description of the Prior Art
Amplification comprises one of the most basic concepts in the art of electronic circuits. Yet, when it comes to efficient, high frequency, high power operation, amplifiers still suffer from distortion, power waste and intermodulation interference problems.
A number of the investigators who have studied the problem have developed interferometric techniques for circumventing the problem. These techniques generally contemplate separating the signal into at least two channels, amplifying the separated signals in constant modulus amplifiers and combining the amplified signals to form the final signal.
M. I. Jacobs in U.S. Pat. No. 3,248,663, issued Apr. 26, 1966, describes a number of interferometric amplifier systems. In one embodiment (FIG. 1), the signal to be amplified is decomposed into two constant amplitude signals with one signal being 180.degree. out of phase with the input and the other signal being also out of phase with the input but with the phase being a function of the amplitude of the input signal. Although recombining these constant amplitude signals forms a signal whose amplitude is proportional to the amplitude of the input signal, the phase of the recombined signal is not in congruence with the phase of the input signal. In another embodiment (FIG. 5), the signal to be amplified is decomposed into two equal, though not constant, amplitude signals symmetrically centered about a signal vector situated 90.degree. away from the input signal. This is achieved by forming the signals x(t)cos(.omega.t-90)+cos.omega.t and x(t)cos(.omega.t-90)-cos.omega.t from the input signal x(t)cos.omega.t. As before (in his FIG. 1), recombining these equal amplitude signals forms a signal whose amplitude is proportional to the amplitude of the input signal but whose phase is not in congruence with that of the input signal. In this embodiment, however, the phase of the developed signal is fixed at 90.degree. away from the input signal.
D. C. Cox in U.S. Pat. No. 3,777,275, issued Dec. 4, 1973, (and in "Component Signal Separation and Recombination for Linear Amplification with Nonlinear Components," IEEE Transactions on Communications, Nov. 1975, pp. 1281-1289) employs the symmetric approach described by Jacobs, but he develops two equal and constant amplitude signals which straddle the input signal. Mathematically, what Cox does can be represented by rewriting the general expression for band limited signals EQU v(t) = x(t) cos[.omega.t+.theta.(t)], (1)
where .omega. is the center frequency and .omega.+.theta.(t) is the instantaneous frequency, in the form EQU v(t) = E{cos[.omega.t+.theta.(t)+.phi.(t)]+cos[.omega.t+.theta.(t)-.phi.(t)]}(2)
where .phi.(t) = cos.sup.-1 [x(t)/2E]; resulting in two constant amplitude signals which lead and lag, respectively, the signal cos[.omega.t+.theta.(t)] by the phase angle .phi.(t). This may better be visualized with reference to FIG. 1, where the signal of Equation (1) is depicted as a rotating signal vector 11 which leads the reference signal vector cos .omega.t by phase angle .theta.(t). Cox decomposes signal vector 11 into signal vectors 12 and 13, of magnitude E, to straddle the input signal. From FIG. 1 it appears clear that the addition of signal vectors 12 and 13 yields the original signal with the correct amplitude and the appropriate phase angle. Signal vectors 12 and 13 are easily constructed by employing a circle of radius 2E, applying a cord at the tip of signal vector 11 which is perpendicular thereto, and extending signal vectors 12 and 13, of magnitude E, toward the intersections of the cord with the circle. It may be observed that for all values of signal vector 11 (of magnitude less than 2E) a set of signal vectors 12 and 13 can always be found and that the accuracy of representing signal vector 11 with signal vectors 12 and 13 depends on the accuracy with which the angle .theta.(t) is known.
In realizing the amplifier, Cox converts the input signal x(t)cos(.omega.t+.theta.( t)) into a constant amplitude signal Ecos(.omega.t+.theta.(t)), phase modulates the constant amplitude signal with +.phi.(t) and -.phi.(t) to develop the two signal vectors 12 and 13, amplifies signal vectors 12 and 13 with constant modulus amplifiers, and combines the amplified signals to form an amplified replica of the input signal.
The Cox approach is very good for signals which can conveniently be hard limited to form the constant amplitude reference Ecos(.omega.t+.theta.(t)). When dealing with modulated signals, however, when the amplitude of the modulated signal has both positive and negative excursions, phase discontinuities occur during zero transitions in the modulated signal's envelope. When hard limiting is undertaken to develop the signal Ecos(.omega.t+.theta.(t)), the phase discontinuities have the same effect, with respect to developed sidebands, as a carrier being modulated by a square wave having very sharp transitions. Because of the extremely wide band developed in the sidebands when a carrier is modulated by a square wave, it can be shown that relatively narrow band determinations lead to significant errors in approximating the signal cos[.omega.t+.theta.(t)].
Another well known decomposition of band limited signals which is described, among others, by D. K. Weaver in "A Third Method for Generation and Detection of Single Sideband Signals," Proceedings of the IRE, Vol. 44, Dec. 1956, pp. 1703-1705, relates the signal of Equation (1) to the two orthogonal signals cos .omega.t and sin .omega.t. That is, Equation (1) is expressed as EQU v(t) = [x(t)cos.theta.(t)]cos.omega.t-[x(t)sin.theta.(t)]sin.omega.t. (3)
This decomposition, which is illustrated in FIG. 2, need not be limited to the orthogonal set sin .omega.t and cos .omega.t. It is valid for any orthogonal set of reference signals, and this includes the set cos(.omega.t+.xi.) and sin(.omega.t+.xi.), where .xi. is zero, fixed, or variable, including a .xi. value approximately equal to Cox's .theta.(t).